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With the development of new, sensitive receivers on submm
telescopes, it has now become possible to study warm, dense
gas directly associated with high-mass star formation in
external galaxies. I shall describe efforts to understand the
correlation of the dense gas tracer, HCN, and bolometric luminosity in term of single-dish surveys (CS, HCN, HCO+,
and N2H+) of galactic high-mass cores. The nearly linear
galactic-extragalactic HCN correlation over 10 orders of magnitude in bolometric luminosity indicates that the star formation rate per unit mass of dense molecular gas is
constant from isolated galactic high-mass cores to the
central regions of ULIRGs.
Understanding the basis for this relation is a current
theoretical challenge. The extragalactic correlation is
also updated for the higher excitation
HCN 3-2 line with observations obtained with the new
single-sideband ALMA 1mm receiver at the SMT 10-m.
The standard extragalactic optical star formation rate tracers,
Ha and OII, are calibrated with respect to the amount of
dense molecular gas.
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